1. September 22, 2014
Review/Practice
Various Equations
Class Work
Questions?
Complete Equations
Handout
New Khan Topics Due
Sunday@ 7:00 pm
Notebooks Collected
This Week
4. This Week @ the Khan Academy:
Two-Step Equations
Equations with Variables on Both Sides
Writing & Interpreting Decimals
@ the V6 Math Site:
Weekly Extra Credit Opportunity: Tuesday’s Teaser
Up Next:
Absolute Value Equations, Opposites & Inverses
And..:
Test #2 Wednesday: All Equations
5. Other Notes..
1. Math Court: Get Registration
forms here; return by Wednesday.
2. Everyone needs service hours to graduate. Hours are
going to be increased from the forty needed now. If you
are interested in tutoring other Algebra I students for
service hour credit, let me know.
3. Please use your notebook as a resource/study
guide, not just as a place to write notes.
6. Warm-Up
Pencils Down, Mental Math
(Pls. Don’t answer until asked)
1. 3x + 5 = 11 2. 2x - 4 = 6 3.
풙
ퟓ
= ퟔ 4.
ퟒ
풙
= ퟐퟒ
1. x = 2 2. x = 5 3. x = 30
5. 3x - 2 = 2x + 6 6. .3x - .2 = .2x + .6
7. .2x - .2 = .3x - .6
4. x =
ퟏ
ퟔ
5. x =8 6. x = 8
7. x = 4
8.
ퟏ
ퟐ
풙 + ퟐ = ퟕ
8. x = 10
Get comfortable, LISTEN, ASK when you are not sure, and
try all of the practice problems. At the end of the period
you should know how to solve the following equations:
(Class Notes Section)
7. Types of Equations
1. One Step 2. Two Step 3. Multi-Step
4. With Variables on both sides
5. With Distribution
6. Equations with Decimals
7. Fractional Equations with one or more Denominators
8. Write & Solve Word Problem Equations
I cannot stress enough how important it is to be able to
solve these equations. Almost every problem we work
this year will at some point involve solving an equation
of the above type. If you are unsure about solving any of
these, you really must listen, ask, and practice.
8. Steps for Solving Equations
(Should be in your notebook. Find it please. If not, rewrite)
1. Clear any fractions/decimals
2. Distribute if necessary.
3. Simplify each side of equation. (Combine like
terms on each side before step four.)
4. Move Constants & Variables to opposite
sides of equation
5. Simplify, divide by coefficient; the result is
your answer.
Write all practice problems in your notebook and try to
solve before solution given.
9. Class Notes & Practice Problems:
Solving Equations using the Distributive Property
-(8d – 7) – 63 = 0 ퟑ
ퟒ
풏 + ퟔ −
ퟏ
ퟐ
(n – 3) = -3
There’s always more than one way to solve a problem.
Solve this by distributing the fractions, not eliminating them.
ퟑ
ퟒ
풏 +
ퟏퟖ
ퟒ
−
ퟏ
ퟐ
풏 +
Multiplying Fractions is easy!!
ퟑ
ퟐ
= -3 N = -36
d = 7
1. 5t - 2(5 + 3t) = 3 + t - 7
5t - 10 - 6t = t - 4
-t - 10 = t - 4 - 6 = 2t; -3 = t
2. -1 – 8(x -6) = 2(2 – 4x + 6)
10. How to Solve Fractional Equations
Solving one denominator equations: The goal is always to
clear the fractions the easiest way possible.
A.
ퟏ
ퟑ
x -
ퟏ
ퟑ
= 9
How many terms are there?
1. Combine like terms if easier. Are there like terms?
Yes. What are they??
Let's not combine them now; 9
2. Instead, let's clear the fractions by multiplying each term
by the number which cancels the denominator
ퟏ
ퟑ
(
ퟏ
ퟑ
x) - (
) = 9 ;
3. Isolate the variable on the left, then divide by any
coefficient.
3
ퟑ
ퟏ
ퟑ
ퟏ
ퟑ
ퟏ
ퟏ
ퟑ
is harder to work with.
Not
ퟏ
ퟑ
x &
ퟏ
ퟑ
!!
x = 28
x - 1 = 27
3
11. Solving Equations with More than one Denominator:
ퟏ
ퟐx - 3 =
ퟏ
ퟓ
x + 3
How many terms are there?
This is one term
1. Since combining like terms is easy this time, do that first.
1/2x = 1/5x + 6
2. Here we have 2 different denominators, so we find the
Least Common Denominator (LCD); The LCD of 2 and 5
is? What is our next step?
Multiply all 3 terms by
ퟏퟎ
ퟏ
; Our equation now looks like:
5x = 2x + 60; Completing the steps we get:
3x = 60; x = 20
10
3
12. Solving Fractional & Decimal Equations
What if…The equation looks like this:
ퟏ
ퟐx - 3 =
ퟏ
ퟓ
(x + 3)
How many terms are there?
(10)
ퟏ
ퟐx – (10)3 = (10)
ퟏ
ퟓ
What is the next step?
(x + 3) 5x – 30 = 2(x + 3);
5x – 30 = 2x + 6; 3x = 36; x = 12
3 + y =
- y
4 8
This equation is actually two equal fractions. Two
equal fractions are called a.....
Proportions can be solve by......
풎
ퟒ
= - 3 m +
ퟐ
ퟑ
=
ퟏ
ퟒ
m - 1
3
13. Clearing Decimals from Equations
Just like fractions, the goal is to eliminate all decimals first.
To clear decimals, you only need to multiply each term by
one of the place values: 10, 100, 100, etc.
Find the term requiring the greatest number of decimal
point moves. Multiply every term by the value corresponding
to the number of decimal point moves.
1. .3x + .4 = .6x + .7 -.5x
2. 0.32x + 0.4 = 0.6x + 0.7 -0.55x
14. Writing/Solving Equations:
1. $270.00 is divided among A, B, and C. B gets twice as
much money as A. C gets $20 more than B. How much does
each receive?
2. Andy is 2 times younger than his sister and his father is
25 years older than him. If the total of their ages is 53
years, what is Andy’s age and his father’s age?
Class Work: Last Section (Word
Problems), changes and solutions
15. Class Work
Work independently or in pairs
For All Assignments:
You Must Show Each Step for Every
Problem.
Example: x + 5 = - 7
x = -7 - 5
x = - 12
-12 + 5 = - 7
